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- W4240909470 abstract "Abstract This chapter discusses parallel dense matrix computations, in particular the solution of linear systems by LU decomposition with partial row pivoting. It first presents a general Cartesian scheme for the distribution of matrices. Based on BSP cost analysis, the square cyclic distribution is proposed as particularly suitable for matrix computations such as LU decomposition and Gaussian elimination. The chapter introduces two-phase broadcasting of vectors, which is a useful collective-communication method for sending copies of matrix rows or columns to a group of processors. It also discusses how to achieve high performance by delaying rank-1 matrix updates to create a multiple-rank update, which can be carried out by multiplying tall-and-skinny matrices in a cache-friendly manner. The high-performance parallel LU decomposition is tested on a top-ranking supercomputer, and its performance is analysed with respect to computation, communication, and synchronization." @default.
- W4240909470 created "2022-05-12" @default.
- W4240909470 creator A5032741850 @default.
- W4240909470 date "2020-09-30" @default.
- W4240909470 modified "2023-10-12" @default.
- W4240909470 title "LU decomposition" @default.
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- W4240909470 doi "https://doi.org/10.1093/oso/9780198788348.003.0002" @default.
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